Problem: Multiply the following complex numbers: $({-2-3i}) \cdot ({1+i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-2-3i}) \cdot ({1+i}) = $ $ ({-2} \cdot {1}) + ({-2} \cdot {1}i) + ({-3}i \cdot {1}) + ({-3}i \cdot {1}i) $ Then simplify the terms: $ (-2) + (-2i) + (-3i) + (-3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -2 + (-2 - 3)i - 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -2 + (-2 - 3)i - (-3) $ The result is simplified: $ (-2 + 3) + (-5i) = 1-5i $